Chords and arclength of a closed space curve
Circular cone and its Gauss map
The family of cones is one of typical models of non-cylindrical ruled surfaces. Among them, the circular cones are unique in the sense that their Gauss map satisfies a partial differential equation similar, though not identical, to one characterizing the so-called 1-type submanifolds. Specifically, for the Gauss map G of a circular cone, one has ΔG = f(G+C), where Δ is the Laplacian operator, f is a non-zero function and C is a constant vector. We prove that circular cones are characterized by being...
Circuminscribed polygons in a plane annulus
Each oval and a natural number n ≥ 3 generate an annulus which possesses the Poncelet's porism property. A necessary and sufficient condition of existence of circuminscribed n-gons in an annulus is given.
Classical differential geometry with Christoffel symbols of Ehresmann -connections
We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christoffel symbols of a symmetric Ehresmann -connection.
Classification der Flächen nach der Transformationsgruppe ihrer geodätischen Curven [Book]
Classification des densités vectorielles factorisées
Classification of complete minimal surfaces in R3 with total curvature 12... .
Classification of five dimensional hypersurfaces with affine normal parallel cubic form.
Classification of homogeneous submanifolds in homogeneous spaces.
Classification of Monge-Ampère equations with two variables
This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.
Classification of pencils of conics of type VI in the isotropic plane. (Klassifikationstheorie der Kegelschnittbüschel vom Typ VI der isotropen Ebene.)
Classification of projective space motions with only plane trajectories
The paper contains the solution of the classification problem for all motions in the complex projective space, which have only plane trajectories. It is shown that each such motion is a submanifold of a maximal motion with the same property. Maximal projective space motions with only plane trajectories are determined by special linear submanifolds of dimensions 2, 3, 5, 8 in , they are denoted as and given by explicit expressions.
Classification of surfaces in which are centroaffine-minimal and equiaffine-minimal.
Clifford algebras and possible kinematics.
Clifford algebras, Möbius transformations, Vahlen matrices, and -loops
In this paper we show that well-known relationships connecting the Clifford algebra on negative euclidean space, Vahlen matrices, and Möbius transformations extend to connections with the Möbius loop or gyrogroup on the open unit ball in -dimensional euclidean space . One notable achievement is a compact, convenient formula for the Möbius loop operation , where the operations on the right are those arising from the Clifford algebra (a formula comparable to for the Möbius loop multiplication...
Clifford fibrations and possible kinematics.
Clifford hypersurfaces in a unit sphere.
Closed space curves of constant curvature consisting of arcs of circular helices.
Closed surfaces with different shapes that are indistinguishable by the SRNF
The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [5], provides a way of representing immersed surfaces in , and equipping the set of these immersions with a “distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of . Thus, it induces a distance function on the shape space of immersions, i.e., the space...
Codazzi structures induced by minimal affine immersions
We give a necessary and sufficient condition for a Codazzi structure to be realized as a minimal affine hypersurface or a minimal centroaffine immersion of codimension two.